How Does a Diffraction Grating Resolve Different Wavelengths of Sodium Light?

[Eagertolearnphysics]

Homework Statement

Yellow sodium light, which consists of two wavelengths, λ_1 =589.0 nm and λ_2 = 589.89 nm, falls on a 7500 lines/cm diffraction grating. Determine (a) the maximum order m that will be present for sodium light, (b) the width of grating necessary to resolve the sodium lines, (c) the grating resolving power in this case, (d) the angular width of each sodium line.

Homework Equations

The Attempt at a Solution

(a) I divided λ by Δλ and I found it to be 1000, therefore Nm, where m is the order, will be always larger than λ/ Δλ. therefore i don't get how the problem asks for maximum, however, m = 1 is an answer!
(b) I tried mλ = d sinθ but i don't know what θ to use !
(c) it depends on (b)

 

[CWatters]

(a) I divided λ by Δλ and I found it to be 1000, therefore Nm, where m is the order, will be always larger than λ/ Δλ. therefore i don't get how the problem asks for maximum, however, m = 1 is an answer!

Perhaps you can explain why you divided λ by Δλ ?

The equation I remember is:
mλ = e * sinθ
where m is the order (1,2,3...)
e is the grating separation
θ is the defraction angle for each m
so
m = e/λ * sinθ

What value of θ gives you maximum m?

 

[Eagertolearnphysics]

Perhaps you can explain why you divided λ by Δλ ?

The equation I remember is:
mλ = e * sinθ
where m is the order (1,2,3...)
e is the grating separation
θ is the defraction angle for each m
so
m = e/λ * sinθ

What value of θ gives you maximum m?

the problem doesn't include the value of θ

 

[Biker]

the problem doesn't include the value of θ

What is the maximum angle you can achieve theoretically?

 

[Eagertolearnphysics]

What is the maximum angle you can achieve theoretically?

π/2

 

[CWatters]

Correct.

So plug that into the equation and calculate m.

 

[Eagertolearnphysics]

Correct.

So plug that into the equation and calculate m.

But I don't have the grating separation

 

[Biker]

You have the number of lines in 1cm.
Can't you use that to find it?

 

[Eagertolearnphysics]

Yes I can, m = 2.26 but I don't know what to do next !

 

[Eagertolearnphysics]

You have the number of lines in 1cm.
Can't you use that to find it?

what is the formula for finding angular dispersion of grating? is it the same as angular width?

 

[CWatters]

Yes I can, m = 2.26 but I don't know what to do next !

You remember that m must be an integer ..